gravitational collapse help needed

[bootsam]

[SIZE=1]i am a little stuck on this, can someone please put me straight

This is from P7 of The Physics of Stars by AC Phillips



g(r)=G m(r)/r^2



which states that each mass element at r moves towards the centre with an acceleration g(r). He then goes on to state that the inward velocity of the element can "be found from the conservation of energy equation."


1/2 [ \frac {dr} {dt} ] ^2 = G m_o /r - G m_o /r_o


Now i know that both sides have been integrated but i thought the integral of



\frac {d^2r} {dt^2} = \frac {dr} {dt}






forgive my tex errors :) the damn things buggy :0

[bootsam]

i shone a red laser through a prism then through the gap on some nail clippers as i reduced the gap manually and onto my wall, the laser dot reduced to a wide straight line as i reduced the clipper gap, brighter in the middle but the line was rotated 90deg to the orientation of the nail clipper slot. why is that? have i just carried out a very inpromptu diffraction experiment?

please forgive my niaivity...i am a novice just embarking on his quest for knowledge